Find the indefinite integral. (use c for the constant of integration.) sech8 x tanh x dx

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Rule [Chain Rule]:                                                                                

Integration

Integrals[Indefinite Integrals] Integration Constant C

Integration Rule [Reverse Power Rule]:                                                              

Integration Property [Multiplied Constant]:                                                        

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u:                                                                                                             [u] Differentiate [Hyperbolic Differentiation, Chain Rule]:                          

Step 3: integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]:                 [Integral] U-Substitution:                                                                              [Integral] Reverse Power Rule:                                                                     Back-Substitute:                                                                                            

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integration

Do you need with the x value for the minimum? its always between the two intercepts for a parabola